the last digit of 3^3^3

Oldest

Best Reply

Author

Message

TAGS:

Manager

Joined: 14 Aug 2009

Posts: 132

Followers: 2

Kudos [?]: 82 [0], given: 13

the last digit of 3^3^3 [#permalink]

18 Aug 2009, 09:00

00:00

Question Stats:

0% (00:00) correct

100% (00:25) wrong

based on 1 sessions

I took the free test of GMAT club. One of the questions is as below.

I choose that "the last digit is 3", but the answer key says "the last digit is 7". The answer key is incorrect, isn't it?

Attachments

2009-08-18_224452.png [ 2.65 KiB | Viewed 700 times ]

_________________

Kudos me if my reply helps!

Kaplan GMAT Prep Discount Codes

Knewton GMAT Discount Codes

Manhattan GMAT Discount Codes

Current Student

Status: What's your raashee?

Joined: 12 Jun 2009

Posts: 1847

Location: United States (NC)

Concentration: Strategy, Finance

Schools: UNC (Kenan-Flagler) - Class of 2013

GMAT 1: 720 Q49 V39

WE: Programming (Computer Software)

Followers: 20

Kudos [?]: 177 [0], given: 52

Re: the last digit of 3^3^3 [#permalink]

18 Aug 2009, 10:26

flyingbunny wrote:

I took the free test of GMAT club. One of the questions is as below.

I choose that "the last digit is 3", but the answer key says "the last digit is 7". The answer key is incorrect, isn't it?

well that reduces into 3^27 right? now you should know the pattern of 3^p is:
1,3,9,7,1,3 etc. starting from p=0. so 28/4 7. So you get to 7. 28 is 27 (1-27) + 1(0th power). It is also simple to count if you really wanted.
Just to clarify - since the pattern for 3^p happens every 4 powers when you divide the power by 4 the remainder determines the position of the digit. In this example .25 = 1, .5=3,.75=9, 1 (or nor remainder) = 7.
_________________

If you like my answers please +1 kudos!

Last edited by shaselai on 18 Aug 2009, 10:30, edited 1 time in total.

CEO

Joined: 29 Aug 2007

Posts: 2528

Followers: 41

Kudos [?]: 364 [0], given: 19

Re: the last digit of 3^3^3 [#permalink]

18 Aug 2009, 10:29

flyingbunny wrote:

I took the free test of GMAT club. One of the questions is as below.

I choose that "the last digit is 3", but the answer key says "the last digit is 7". The answer key is incorrect, isn't it?

Follow here: last-digit-of-a-power-70624.html

You find some good discussions and concepts.
_________________

Verbal: new-to-the-verbal-forum-please-read-this-first-77546.html
Math: new-to-the-math-forum-please-read-this-first-77764.html
Gmat: everything-you-need-to-prepare-for-the-gmat-revised-77983.html

GT

Manager

Joined: 14 Aug 2009

Posts: 132

Followers: 2

Kudos [?]: 82 [0], given: 13

Re: the last digit of 3^3^3 [#permalink]

18 Aug 2009, 11:30

http://en.wikipedia.org/wiki/Exponentiation

according to this, the answer of "the last digit of 3^3^3" should be 7.

if you know the sequence of computing exponentiation, this question is a piece of cake, otherwise you would never get the answer right.
_________________

Kudos me if my reply helps!

Re: the last digit of 3^3^3 [#permalink] 18 Aug 2009, 11:30

		Similar topics	Author	Replies	Last post
Similar Topics:		Find the units digit of 333^333 have fun	MBA04	11	25 Jun 2003, 13:28
		Find is the last digit of 3^(3^3) ? A) 1 B) 7 C) 6 D) 3 E) 5	briozeal	8	12 Nov 2005, 11:48
	92	What is the last digit 3^{3^3} ? A. 1 B. 3 C. 6 D. 7 E. 9	elmagnifico	67	23 Sep 2008, 07:17
		What is the last digit 3^{3^3} ? * 1 * 3 * 6 * 7 * 9	study	4	19 Oct 2008, 00:44

the last digit of 3^3^3

Main navigation

GMAT Resources

Partners

MBA Resources

GMAT ® is a registered trademark of the Graduate Management Admission Council ® (GMAC ®). GMAT Club's website has not been reviewed or endorsed by GMAC.

GMAT Courses

Admissions Consulting

the last digit of 3^3^3

the last digit of 3^3^3

Main navigation

GMAT Resources

Partners

MBA Resources